ARK: Robust Knockoffs Inference with Coupling

• URL: http://arxiv.org/abs/2307.04400v2
• Date: Tue, 4 Jun 2024 23:50:58 GMT
• Title: ARK: Robust Knockoffs Inference with Coupling
• Authors: Yingying Fan, Lan Gao, Jinchi Lv,
• Abstract summary: We study the robustness of the model-X knockoffs framework with respect to the misspecified or estimated feature distribution. A key technique is to couple the approximate knockoffs procedure with the model-X knockoffs procedure so that random variables in these two procedures can be close in realizations. We prove that if such a coupled model-X knockoffs procedure exists, the approximate knockoffs procedure can achieve the FDR or $k$-FWER control at the target level.
• Score: 7.288274235236948
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the robustness of the model-X knockoffs framework with respect to the misspecified or estimated feature distribution. We achieve such a goal by theoretically studying the feature selection performance of a practically implemented knockoffs algorithm, which we name as the approximate knockoffs (ARK) procedure, under the measures of the false discovery rate (FDR) and $k$-familywise error rate ($k$-FWER). The approximate knockoffs procedure differs from the model-X knockoffs procedure only in that the former uses the misspecified or estimated feature distribution. A key technique in our theoretical analyses is to couple the approximate knockoffs procedure with the model-X knockoffs procedure so that random variables in these two procedures can be close in realizations. We prove that if such coupled model-X knockoffs procedure exists, the approximate knockoffs procedure can achieve the asymptotic FDR or $k$-FWER control at the target level. We showcase three specific constructions of such coupled model-X knockoff variables, verifying their existence and justifying the robustness of the model-X knockoffs framework. Additionally, we formally connect our concept of knockoff variable coupling to a type of Wasserstein distance.

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